Question

Find a Quadratic equation whose roots are 1.5+√2 and 1.5-√2​

Answer 1

x² - 3x + 0.25 = 0

Explanation:

Given a root x = a then the corresponding factor is (x - a)

Given roots x = 1.5 +
`√(2)` and x = 1.5 -
`√(2)` then the factors are

(x - (1.5 +
`√(2)` ) ) and (x - (1.5 -
`√(2)` ) ) , that is

(x - 1.5 -
`√(2)` ) and (x - 1.5 +
`√(2)` )

The equation is then the product of the factors

(x - 1.5 -
`√(2)` )(x - 1.5 +
`√(2)` ) = 0 ← expand factors using FOIL

(x - 1.5)² - (
`√(2)` )² = 0

x² - 3x + 2.25 - 2 = 0

x² - 3x + 0.25 = 0